The Variational Sequence on Finite Jet Bundle Extensions and the Lagrangian Formalism

Details The Variational Sequence on Finite Jet Bundle Extensions and the Lagrangian Formalism The Variational Sequence on Finite Jet Bundle Extensions and the Lagrangian Formalism

1997-02-18

arxiv.org/abs/dg-ga/9702016v2

Physics

High Energy Physics

High Energy Physics - Theory

67 pages, many improvements, some proofs are presented in more detail

Scientific paper

The geometric Lagrangian theory (of arbitrary order) is based on the analysis of some basic mathematical objects such as: the contact ideal, the (exact) variational sequence, the existence of Euler-Lagrange and Helmholtz-Sonin forms, etc. In this paper we give new and much simpler proofs for the whole theory using Fock space methods. Using these results we give the most general expression for a variationally trivial Lagrangian and the generic expression for a locally variational system of partial differential equation.

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